In the field of automobile research and development, a variety of estimation methods using a computer-aided CAE technology have been proposed progressively for minimizing the weight of vehicles, the length of time for the development, and the number of prototype vehicles. Among of them is estimation of the physical strength of a vehicle which has also been vigorously studied.
The body of a vehicle is generally fabricated by sheet metals. The sheet metals are commonly joined together by spot welding. During the spot welding, the vehicle receives loads which are then transmitted through the welding contacts to every part of the components. In particular, the loads may be intensified at the welding contacts thus declining the physical strength of the vehicle. As the number of the welding contacts is large and the loads are composite or varied in the characteristics, the demand for developing a method of estimating the fatigue life of the spot welding contacts accurately and readily will now be increased.
In response to the demand, a technique for estimating the fatigue life of spot welding contacts is proposed by Dieter Radaj, et al., as disclosed in “Design and Analysis of Fatigue Resistant Welded Structures”, Abington Publication, P. 378, 1990, where a disk, D in diameter, having a nugget at the center and separated from the spot welded structure of a vehicle is subjected to FEM shell analysis for calculating the nominal structural stress σns from partial loads on the nugget and settings of the diameter D saved in a database, whereby the fatigue life of the spot welded structure can be estimated from the nominal structural stress. The fatigue/reliability group of the automobile technology committee has also proposed a similar method concerning the effect of torsion on the structure. The nominal structural stress σns is a maximum main stress produced at the spot welding contact (nugget).
Each of the methods includes, as shown in FIG. 22, a step S1 of fabricating a spot welded structure, a step S2 of preparing a finite element method analyzing shell model (FEM model) and providing the FEM model with a load data D1, a step S3 of determining six partial forces of the load exerted at the spot welded contact (nugget), a step S4 of calculating the nominal structural stress σns with settings of D saved in a database D2, and a step S5 of estimating the fatigue life through examining the nominal structural stress σns with a map of database D3 representing the relationship between the nominal structural stress σns and the number of cycles to fracture Nf.
However, both the conventional methods allow the nominal structural stress σns to be calculated using a disk bending theory of the elastodynamics on a disk, D in diameter, as a rigid body having a nugget designated at the center thereof while peel load and bending moment of the partial forces are concerned. The circumferential condition for the disk is based on the fact that no deflection nor tilting in any radial direction is involved as is termed an entire-freedom arresting condition. It is hence not easy for calculating the nominal structural stress σns on the disk of spot welded structure to determine an optimum of the diameter D of the disk. In the prior art, the diameter D is determined from a database D2 as shown in a flowchart of FIG. 22. It is true that the preparation of the database D2 is also a labor intensive task.
FIG. 23 illustrates a disk 2, D in diameter, separated from a spot welded structure and having a nugget 1 (spot welded contact) designated at the center thereof. The nugget 1 generally receives six partial loads;
1. peel load Fz,
2. bending moments Mx, My,
3. shearing loads Fx, Fy, and
4. torsional moment Mz.
The method by Dieter Radaj et al calculates the nominal structural stress σns, which is a fatigue strength parameter responsive to particularly the torsional moment and the peel load of the six partial loads exerted on the nugget, using the following elements,
(1) Peel load
      σ    ns    =      0.69    ⁢          (                        F          z                          t          2                    )        ⁢          ln      ⁡              (                  D          d                )            
(2) Bending moment
      σ    ns    =      25.4    ⁢          (              M                  dt          2                    )        ⁢                  (                  d          D                )            /              ⅇ                  4.8          ⁢                      d            D                              where D, d, and t are the outer diameter, of the disk 2 having the nugget 1 provided in the center, the diameter of the nugget 1, and the thickness of the disk 2 as shown in FIG. 23 and Fz and M are the peel load and the bending moment exerted on the nugget 1.
Equations 1 and 2 are based on the fact that the disk 2 shown in FIG. 23 has the nugget 1 as a rigid body and is perfectly arrested at the circumference for no strain.
Accordingly, only when the perfect arresting condition for no strain is satisfied, the diameter D may be determined with a favorable setting for calculating the nominal structural stress σns on a spot welded structure from Equations 1 and 2 and estimating the fatigue life. There may however be seldom the case where the area about the nugget 1, D in diameter, in an actual spot welded structure remains perfectly arrested for no strain. Therefore, it will be a drawback for calculation of the equations to determine the diameter D of the disk 2 to an optimum.
It is assumed for examining the stress responsive to the shearing load Fx and Fy that the shearing load Fx is exerted in the x direction on the center as circular rigid body of an infinite plate which has a diameter of d and acts as a nugget. The stress component σx along the x direction off the rigid body is then expressed by:
                                          σ            x                    =                                                    -                                  F                  x                                                            2                ⁢                                                                  ⁢                π                ⁢                                                                  ⁢                                  t                  ⁡                                      (                                          κ                      +                      1                                        )                                                                        ⁢                          1              x                        ⁢                          {                                                (                                      κ                    -                                                                  1                        2                                            ⁢                                                                        d                          2                                                                          x                          2                                                                                                      )                                +                3                            }                                      ⁢                                  ⁢                  κ          =                                                    (                                  3                  -                  v                                )                            /                              (                                  1                  +                  v                                )                                      ⁢                                                  ⁢                                                          (        3        )            where ν is the Poisson's ratio. As the nominal structural stress is a maximum main stress at the edge of the nugget,
                              σ          x                =                              F            x                                π            ⁢                                                  ⁢            dt                                              (        4        )            
FIG. 24 illustrates a profile of the stress distribution vertical to the loading direction on the outer surface of the center plate of three plates which have been spot welded together and loaded with a tensile shearing force, where σo is the uniform tensile stress. As apparent, the theoretical result of Equation 3 as the nominal structural stress is closely approximate to the result of FEM three-dimensional elastodynamics analysis at the point close to the nugget. However, the difference between the two results is gradually increased as the point departs from the edge of the nugget. The reason is because Equation 3 approximates zero at the furthest point from the nugget and fails to exhibit the result of the stress σo at the point close to the nugget.
For example, when a doughnut shaped disk is urged by external pressures from both, outer and inner, sides, its resultant stress is expressed by a particular profile of the distribution. The stress is calculated from:
                              σ          r                =                                            a              2                                                      b                2                            -                              a                2                                              [                                                    (                                  1                  -                                                            b                      2                                                              r                      2                                                                      )                            ⁢                              p                                  i                  ⁢                                                                          ⁢                  n                                                      -                                          (                                                                            b                      2                                                              a                      2                                                        -                                                            b                      2                                                              r                      2                                                                      )                            ⁢                              p                                  σ                  ⁢                                                                          ⁢                  t                                                              ]                                    (        5        )                                          σ          r                =                              -                                          a                2                                            r                2                                              ⁢                      p                          i              ⁢                                                          ⁢              n                                                          (        6        )            
FIG. 26 illustrates comparison between the above profile and its comparative profile from Equation 6 where the doughnut shaped disk is replaced by an infinite plate having an opening provided therein. When the outer pressure is smaller than the inner pressure, the former profile may be similar to the latter profile of the infinite plate. However, when the two, outer and inner, pressures are substantially equal, the stress profiles will significantly be different from each other. This phenomenon may appear in the profile of the stress distribution shown in FIG. 24 where the three plates are spot welded together. It will hence be difficult to calculate the stress at higher accuracy through comparison with that of the infinite plate.
FIG. 27 illustrates a profile of the stress distribution vertical to the loading direction where two, large and small, flat plates are joined to each other by spot welding to simulate a bracketed spot welded joint and loaded at both sides with uniform tensile stresses σo. Since the welded plates remain balanced, the partial loads on the nugget will be zero at the finite element method analysis using a shell element model. It is thus understood that Equation 3 is unfavorable for determining the stress for the case.
It is hence an object of the present invention to provide a fatigue life estimating method for a spot welded structure in which the nominal structural stress is calculated from the deflection, the tilting in one radial direction, the bending moment, the peel load, the shearing force, and the torsional moment on a disk to be examined for optimizing the setting of D and the fatigue life of the disk or spot welded structure is estimated using the nominal structural stress.
It is another object of the present invention to provide a novel method of solving the drawback that as the point to be measured departs from the edge of the nugget, its uniform load tensile stress is increased in the erratic measurement.